Inroduction to Special Topics in Business Economics Technical - PowerPoint PPT Presentation

Department of Economics University of Patras, Greece Inroduction to Special Topics in Business Economics ”Technical Efficiency (TE) in R” Using Data Envelopment Analysis (DEA) under different technology assumptions PhD Candidate: Eirini Stergiou e . stergiou @ upnet . gr School of Business Administration Department of Economics University of Patras, Greece November 10, 2018 Applied Economics & Data Analysis Department of Economics November 10, 2018 1 / 13

Department of Economics University of Patras, Greece Structure 1 Efficiency measure Introduction Benchmarking package One Input - One Output Two Inputs - One Output Example with a dataset Applied Economics & Data Analysis Department of Economics November 10, 2018 2 / 13

Efficiency measure Introduction Input orientation:”By how much can input quantities be proportionally reduced without changing the output quantities produced?” Output orientation:”By how much can output quantities be proportionally increased without changing the input quantities used?” CRS - VRS assumption One advantage of the Farrell input and output orientated radial TE measures is that they are units invariant DEA is the non-parametric mathematical programming approach to frontier estimation Charnes, Cooper and Rhodes (1978) proposed a model which had an input orientation and assumed CRS Banker, Charnes and Cooper (1984) proposed a VRS model Second stage of linear programming by maximizing the sum of slacks (e.g. Ali and Seiford (1993)) However some problems occur (furthest efficient point,not unit invariant) Applied Economics & Data Analysis Department of Economics November 10, 2018 3 / 13

Efficiency measure Benchmarking package We use the Benchmarking package It contains an extensive number of methods for parametric and nonparametric efficiency analysis It offers a variety of DEA methods and it is easy to use plotting facilities Applied Economics & Data Analysis Department of Economics November 10, 2018 4 / 13

Efficiency measure One Input - One Output x: Labor y: Sales CRS - calculate the ratio of output to input DMU B has the highest ratio Dividing all ratios by the maximal ratio = ⇒ efficiency scores A B C D E Input x 1.000 2.000 3.000 4.000 5.000 Output y 1.000 3.000 2.000 5.000 4.000 y/x 1.000 1.500 0.667 1.250 0.800 Efficiency 0.667 1.000 0.444 0.833 0.533 We can benchmark all DMUs indexed by i relative to the efficient DMU B 0 ≤ Sales per employee of DMU i ≤ 1 (1) Sales per employee of B Applied Economics & Data Analysis Department of Economics November 10, 2018 5 / 13

Efficiency measure One Input - One Output Figure 1: One input - one output case Applied Economics & Data Analysis Department of Economics November 10, 2018 6 / 13

Efficiency measure One Input - One Output Coding install.packages(”Benchmarking”) library(Benchmarking) emp < − matrix(1:5) sales < − matrix(c(1,3,2,5,4)) nam < − LETTERS[1:5] maxc < − cmax(sales/emp) eff < − sales/emp / max tab < − t(round(cbind(emp,sales,round(sales/emp,3),eff),3)) colnames(tab) < − nam rownames(tab) < − c(”input x”,”output y”,”y/x”,”efficiency”) View(tab) dea.plot(emp,sales,RTS=”crs”,ORIENTATION=”in- out”,pch=19,cex=0.8,txt=LETTERS[1:length(emp)],las=1) Applied Economics & Data Analysis Department of Economics November 10, 2018 7 / 13

Efficiency measure Two Inputs - One Output x 1 : Employees x 2 : Floor area y: Sales CRS Isoquant curve A B C D E Input x 1 4.000 7.000 8.000 5.000 2.000 Input x 2 3.000 2.000 1.000 5.000 5.000 Output y 1.000 1.000 1.000 1.000 1.000 Efficiency 1.000 0.909 1.000 0.700 1.000 The three efficient units A, C, and E serve as the benchmark for the non-efficient DMUs. Applied Economics & Data Analysis Department of Economics November 10, 2018 8 / 13

Efficiency measure Two Inputs - One Output Figure 2: Two inputs - one output case Applied Economics & Data Analysis Department of Economics November 10, 2018 9 / 13

Efficiency measure Two Inputs - One Output Coding x1 < − c(4,7,8,5,2) x2 < − c(3,2,1,5,5) y < − rep(1,5) X < − cbind(x1,x2) Y < − matrix(y) e < − dea(X,Y,RTS=”crs”,ORIENTATION=”in”,SLACK=T) eff(e) plot < − dea.plot.isoquant(x1,x2,txt=LETTERS[1:5], xlim=c(0,10),pch=19,cex=0.8) Applied Economics & Data Analysis Department of Economics November 10, 2018 10 / 13

Efficiency measure Example with a dataset Dataset charnes1981 A data frame with 70 school sites firm: school site number x1: education level of the mother x2: highest occupation of a family member x3: parental visits to school x4: time spent with children in school-related topics x5: the number of teachers at the site y1: reading score y2: math score y3: self - esteem score pft: =1 if in program (program follow through) and =0 if not in program name: Site name Applied Economics & Data Analysis Department of Economics November 10, 2018 11 / 13

Efficiency measure Example with a dataset Coding Reading a file charnes1981 < − read.csv(”C:/Users/Irene/Documents/R/win- library/3.4/Benchmarking/data/charnes1981.csv/charnes1981.csv”, header=TRUE, sep=”;”) x < − with(charnes1981, cbind(x1,x2,x3,x4,x5)) y < − with(charnes1981, cbind(y1,y2,y3)) Phase one: Farrell input efficiency - vrs technology e < − dea(x, y, RTS=”vrs”, ORIENTATION=”in”) peers(e) lambda(e) summary(e) excess(e,x) Phase two: Calculate slacks (maximize sum of slacks) el < − dea(x,y,SLACK=TRUE) Creating a data frame total < − data.frame(e$eff,el$slack,el$sx,el$sy) Saving the efficiency results write.csv(total, file = ”C:/Users/Irene/Desktop/efficiency.csv”) Applied Economics & Data Analysis Department of Economics November 10, 2018 12 / 13

Efficiency measure Example with a dataset References Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078-1092. Charnes, A., Cooper, W. W., & Rhodes, E. (1981) Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through. Management Science, 27(6), 668-697. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444. Peter Bogetoft and Lars Otto. Benchmarking with DEA, SFA, and R, Springer 2011. Sect. 5.2 page 115 P Andersen and NC Petersen. ”A procedure for ranking efficient units in data envelopment analysis”, Management Science 1993 39(10):1261-1264 https://cran.r-project.org/web/packages/Benchmarking/ Benchmarking.pdf Applied Economics & Data Analysis Department of Economics November 10, 2018 13 / 13